Page 200 of the DMG states:
If the spell is on your class's spell list you can use an action to read the scroll and cast its spell
So if a wizard were to pick up a spell scroll containing a wizard spell, the wizard would be able to identify it
Later in the same paragraph it also states:
Otherwise, the scroll is unintelligible.
So if the wizard were to pick up a sorcerer spell,the wizard wouldn't be able to read it.
In conclusion if the spell is on the reader's spell list then the reader would be able to identify it.